Effective algorithm for ray-tracing simulations of lobster eye and similar reflective optical systems

Abstract

The algorithm presented is intended mainly for lobster eye optics. This type of optics (and some similar types) allows for a simplification of the classical raytracing procedure that requires great many rays to simulate. The method presented performs the simulation of a only few rays; therefore it is extremely effective. Moreover, to simplify the equations, a specific mathematical formalism is used. Only a few simple equations are used, therefore the program code can be simple as well. The paper also outlines how to apply the method to some other reflective optical systems.

Effective collecting area of lobster eye optics and optimal value of effective angle

“…Moreover, we added reflectivity as it is outlined in the paper [19]. As in papers [4,12,17,19,20], the problem of one-dimensional lobster eye stack is analysed in cross-section and the geometry becomes just twodimensional.…”

“…Smoothed step model shown in Fig. 6c with parameters mentioned in the previous section was chosen to be compared with results of numerical simulations based on simplified ray-tracing algorithm (SRTA) [20]. This simulation method is exact.…”

“…For numerical simulations of lobster eye optics, a general ray-tracing approach is possible, see e.g. [13] or its simplified procedures [20,21]. Analytic models represents another type of computation.…”

Optimization of mirror spacing or pore width of lobster eye optics

“…As in several papers (Chapman et al 1991;Schmidt 1975;Su et al 2017;Tichý et al 2015bTichý et al , 2016, the problem of a single LE stack is analyzed in the cross-sectional plane. The geometry of the stack is described by the following parameters ( Figure 1): radius of the system r; middle mirror spacing from surface to surface (pore width) a; mirror thickness (pore wall width) t, mirror (pore) depth h, and the number of mirrors N. The parameter ≈ arctan(a/h) ≈ a/h is called the effective angle (Inneman 2001;Schmidt 1975;Tichý et al 2015b).…”

“…For numerical simulations of LE optics, the general ray-tracing approach is possible (see, e.g., Spencer & Murty 1962) or its simplified versions (Šaroun & Kulda 2006;Tichý et al 2016).…”